The Whitham equation for hydroelastic waves
The Whitham equation for hydroelastic waves
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DOI：
10.1016/j.apor.2019.04.026
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发表时间：
2019-08-01
影响因子：
4.3
通讯作者：
Parau, Emilian I.
中科院分区：
文献类型：
--
作者：
Dinvay, Evgueni;Kalisch, Henrik;Parau, Emilian I.
本文导出了一个弱非线性全频散模型方程，它描述了波在覆盖不可压缩无粘流体的薄弹性体中的传播。该方程的线性部分是非局部的，类似于描述无粘流体自由表面波动的Whitham方程，数值逼近了完全非线性水弹性Euler方程的定常解，并与完全色散但弱非线性模型方程稳态解的数值逼近进行了比较，得到了这些方程的分岔曲线两种不同的模式进行了比较，发现弱非线性模式给出了准确的预测波的小到中等幅度。对于较大振幅的波，这两个模型仍然同意关键的定性特征，如分叉点，二次分叉，在一个给定的基波周期的振荡数。
A weakly nonlinear fully dispersive model equation is derived which describes the propagation of waves in a thin elastic body overlying an incompressible inviscid fluid. The equation is nonlocal in the linear part, and is similar to the so-called Whitham equation which was proposed as a model for the description of wave motion at the free surface of an inviscid fluid.Steady solutions of the fully nonlinear hydro-elastic Euler equations are approximated numerically, and compared to numerical approximations to steady solutions of the fully dispersive but weakly nonlinear model equation.The bifurcation curves for these two different models are compared, and it is found that the weakly nonlinear model gives accurate predictions for waves of small to moderate amplitude. For larger amplitude waves, the two models still agree on key qualitative features such as the bifurcation points, secondary bifurcations, and the number of oscillations in a given fundamental wave period.